Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

DOI10.1016/j.physleta.2020.126530zbMath1448.81345arXiv2004.05612OpenAlexW3016109012MaRDI QIDQ2213175

Rebecca Tenney, Andreas Fring

Publication date: 30 November 2020

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.05612

zbMATH Keywords

non-Hermitian quantum mechanicsanharmonic oscillators\(\mathcal{PT}\)-symmetric quantum mechanicsdouble wells

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Alternative quantum mechanics (including hidden variables, etc.) (81Q65)

Related Items (6)

Real energies and Berry phases in all PT-regimes in time-dependent non-Hermitian theories ⋮ Exactly solvable time-dependent non-Hermitian quantum systems from point transformations ⋮ Time-dependent \(\mathcal{C}\)-operators as Lewis-Riesenfeld invariants in non-Hermitian theories ⋮ Hybrid form of quantum theory with non-Hermitian Hamiltonians ⋮ Systematics of quasi-Hermitian representations of non-Hermitian quantum models ⋮ Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians

Cites Work

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• Mending the broken PT-regime via an explicit time-dependent Dyson map
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• Time-dependent $\mathcal {P}$$\mathcal {T}$-symmetric quantum mechanics
• PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS
• Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory
• Equivalence of unstable anharmonic oscillators and double wells
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Solvable two-dimensional time-dependent non-Hermitian quantum systems with infinite dimensional Hilbert space in the broken PT-regime
• Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems
• Time-dependent metric for the two-dimensional, non-Hermitian coupled oscillator
• Time evolution of non-Hermitian Hamiltonian systems

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